Write the equation of the parabola that passes through the points (–4,0), (–2,0), and (–1,–15).Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions.
Question
Write the equation of the parabola that passes through the points (–4,0), (–2,0), and (–1,–15).Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions.
Solution
To find the equation of the parabola that passes through the points (-4,0), (-2,0), and (-1,-15), we can use the form y=a(x–p)(x–q), where a, p, and q are the x-intercepts of the parabola.
From the given points, we can see that the x-intercepts are -4 and -2. Therefore, p and q are -4 and -2. So, the equation becomes:
y = a(x - (-4))(x - (-2))
Simplify to:
y = a(x + 4)(x + 2)
Now, we need to find the value of 'a'. We can use the third point (-1,-15) for this. Substitute x = -1 and y = -15 into the equation:
-15 = a(-1 + 4)(-1 + 2)
Simplify to:
-15 = a(3)(1)
-15 = 3a
Solve for 'a':
a = -15 / 3
a = -5
So, the equation of the parabola is:
y = -5(x + 4)(x + 2)
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